Definition:Sigma-Ring/Definition 1

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A $\sigma$-ring is a ring of sets which is closed under countable unions.

That is, a ring of sets $\Sigma$ is a $\sigma$-ring if and only if:

$\ds A_1, A_2, \ldots \in \Sigma \implies \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma$

Also see

Linguistic Note

The $\sigma$ in $\sigma$-ring is the Greek letter sigma which equates to the letter s.

$\sigma$ stands for for somme, which is French for union.